用可学习的分数阶导数分布建模图神经网络，捕捉复杂动态。
Distributed-Order Fractional Graph Operating Network
- 引入可学习的分布式分数阶导数，替代传统整数或单分数阶微分。
- 在多个图学习任务中表现优于传统连续图神经网络。
- 适合研究复杂图动态、需建模非马尔可夫过程的场景。
我们提出分布式阶分数阶图操作网络（DRAGON），一种新型的连续图神经网络框架，融合分布式阶分数阶微积分。与使用整数阶或单一分数阶微分方程的传统连续图神经网络不同，DRAGON在实数范围上引入可学习的概率分布来表示导数阶数。通过灵活且可学习的多阶导数叠加机制，该框架能捕捉超越传统模型的复杂图特征更新动态。我们从非马尔可夫图随机游走视角解释其能力，节点特征更新由图上的异常扩散过程驱动。为验证框架的通用性，我们在多种图学习任务上进行实验，结果一致表明其性能优于传统连续图神经网络模型。实现代码见： https://github.com/zknus/NeurIPS-2024-DRAGON。
原文摘要 · Abstract (English)
We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.
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